Such hydraulic pressure regulators generally comprise a centrifugal governor in a mounting which is fixedly secured to a shaft whose speed is to be monitored, such as an output shaft of a planetary-gear train in a transmission system of an automotive vehicle. A valve included in that governor controls the flow of a hydraulic fluid whose pressure downstream of that valve is used as a parameter which codetermines the shifting operations together with other factors. In conventional systems of this type, e.g. as described in U.S. Pat. No. 3,095,755, the hydraulic fluid is supplied to the governor and returned from it by way of respective bores in the shaft. Such an arrangement, of course, weakens the shaft and therefore requires an enlargement of its diameter for the transmission of a given torque. Other known constructions, designed to avoid a weakening of the shaft, generally result in larger overall dimensions of the regulator assembly.